Theory of size mismatched alloy systems: many-body Kanzaki forces

A perturbative approach to determining the strain-induced effective interactions in binary alloys with large atomic size mismatch is presented. Using the chemical energy as the reference state, the strain-induced energy of the alloy is cast into a many-body (Kanzaki) force expansion that depends on both the configurational and displacive degrees of freedom. It is shown that the k-space energy expansion is valid for all wavelengths. The theory is then applied to the Cu3Au alloy where, due to the large difference between atomic sizes, considerable relaxations are observed from first-principles calculations. We found that the inhomogeneous contribution () dominates the strain energy in Cu3Au, whereas the homogeneous part (k = 0), notwithstanding its configurational dependence, contributes only a few per cent.